Journal article
On isometries of operator algebras
Journal of functional analysis, Vol.119(1), pp.138-170
1994
DOI: 10.1006/jfan.1994.1006
Abstract
We study the Banach space isometries of triangular subalgebras of C*-algebras that contain diagonals in the sense of Kumjian. Under a mild technical assumption, we prove that every isometry between two such algebras decomposes as a direct sum of a unitary multiple of an isometric algebra isomorphism and a unitary multiple of an isometric algebra anti-isomorphism. Moreover, each isometric algebraic isomorphism (anti-isomorphism) between two algebras of the type considered here extends to a C*-isomorphism (C*-anti-isomorphism) between the enveloping C*-algebras. Our hypotheses enable us to "coordinatize" the algebras under consideration, and the structure of the isometries between the algebras is expressed in terms of the coordinates.
Details
- Title: Subtitle
- On isometries of operator algebras
- Creators
- P. S MUHLY - Univ. Iowa City, dep. mathematics, Iowa City IA 52242, United StatesCHAOXIN QIU - Univ. Iowa City, dep. mathematics, Iowa City IA 52242, United States
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.119(1), pp.138-170
- DOI
- 10.1006/jfan.1994.1006
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- Academic Press
- Language
- English
- Date published
- 1994
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984083892702771
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